Gong S., Gong Y. — Concise Complex Analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Gong S., Gong Y. — Concise Complex Analysis

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Название: Concise Complex Analysis

Авторы: Gong S., Gong Y.

Аннотация:

A concise textbook on complex analysis for undergraduate and graduate students, this book is written from the viewpoint of modern mathematics: the Bar {Partial}-equation, differential geometry, Lie groups, all the traditional material on complex analysis is included. Setting it apart from others, the book makes many statements and proofs of classical theorems in complex analysis simpler, shorter and more elegant: for example, the Mittag-Leffer theorem is proved using the Bar {Partial}-equation, and the Picard theorem is proved using the methods of differential geometry

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 237

Добавлена в каталог: 02.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Abel theorem      26
Ahlfors — Schvvarz lemma      151
Analytic continuation      113
Analytic element      116
Analytic function      12
Annulus of convergence      87
Argument      9
Argument principle      60
Ascoli — Arzela theorem      129
Automorphic function      205
Basic quasi periods      196
Bernulli number      215
Biholomorphic      169
Biholomorphic automorphism      174
Biholomorphic mapping      124
Blaschke product      118
Bloch theorem      161
Bolzano — Weierstrass theorem      12
Branch point      137
Caratheodory inequality      141
Cartan theorem      172
Cauchy Criterion for Convergence      26
Cauchy inequality      55
Cauchy integral formula      41
Cauchy integral formula for the outside region of a simple closed curve      76
Cauchy integral theorem      41
Cauchy kernel      69
Cauchy — Goursat integral formula      44
Cauchy — Goursat integral theorem      44
Cauchy — Green formula      39
Cauchy — Riemann equations      13
Chebyshev function      219
Circular domain      173
Complete analytic function      117
Conformal mapping      123
Conformality      17
Congruence subgroup      205
Congruent      200
conjugate      8
Conjugate Poisson kernel      72
Cross ratio      126
Curvature      145
de Moivre formula      21
Derivative      12
Different iable      12
Disc of convergence      27
Domain of holomorphy      184
Elliptic integral      200
Elliptic metric      148
Entire function      93
Equibounded      129
Equicontinuous      129
Essential singularity      91
Euclidean distance      146
Euclidean metric      146
Euler formula      20 212
Euler reflection formula      210
Existence domain      117
Exterior differential form      6 18
Exterior differential operator      6
Exterior product      6 18
Factorization      97
Fundamental domain      203
Fundamental parallelogram      18C
Fundamental theorem of algebra      59
Fundamental theorem of calculus      2
Gamma function      207
Gauss's theorem      5
Gaussian curvature      165
Global analytic function      117
Global holomorphic function      117
Great Picard theorem      160
Green’s Theorem      5
Group of Euclidean motions      146
Group of holomorphic automorphisms      66
Group of holomorphic automorphisms on the unit disc      67
Group of Mobius transformations      96
Group of rigid motions      146
Hadamard’s formula      27
Hadamard’s three circles theorem      80
Harmonic function      15
Hartogs phenomenon      181
Hartogs theorem      181
Hartogs theorem on Reinhardt domains      183
Hausdorff space      143
Heine — Borel theorem      12
Holomorphic automorphism      66
Holomorphic coordinate covering      143
Holomorphic function      12
Holomorphic local coordinate system      143
Holomorphic mapping      123
Holomorphically equivalent      128
Homeomorphism      143
Hurwitz theorem      61
Hyperbolic metric      146
Ikehara Theorem      226

Integral of Cauchy type      77
Interpolation theorem      105
Jordan curve      11
Jordan theorem      11
Landau theorem      161
Laplace equation      15
Laurent series      86
Legendre relation      196
Liouville theorem      57
Little Picard theorem      154
Locally analytic      116
Locally holomorphic      116
Logarithm      22
Marty criterion      157
Maximum Modulus Principle      65
Mean curvature      165
Mean value theorem      3
Meromorphic function      94
Metric      145
Mittag — Leffler theorem      102
Modular constant      199
Modular function      205
Modular group      200
Modulus      9
Moebius transformation group      67
Montel theorem      129 157
Morera theorem      57
Multiply connected      12
Normal curvature      165
Normal family of functions      129
Order of an elliptic function      189
Painleve theorem      134
Parabolic metric      146
Partition of unity theorem      83
Piecewise smooth curve      11
Poincare lemma      7
Poincare metric      146
Poincare theorem      179
Poincare — Koebe theorem      96
Poisson integral formula      70
Poisson kernel      70
Poisson — Jensen formula      118
Pole      91
Polydisc      169
Ponipeiu formula      39
Prime number theorem      219
Principle argument      9
Principle branch      23
Principle curvatures      165
Principle direction      165
Reabe criterion      36
Region      11
Reinhardt domain      181
Removable singularity      90
Residue      106
Residue theorem      107
Riemann $\zeta$ -function      211
Riemann mapping theorem      128
Riemann sphere      10
Riemann Theorem      58
Rotation group      67
Rouche theorem      62
Schottky theorem      161
Schvvarz kernel      71
Schvvarz lemma      66
Schvvarz — Pick lemma      68
Schwarz — Christoffel formula      140
Simple curve      11
Simple pole      91
Simply connected      12
Singularity      114
Slowly decreasing function      224
Smooth curve      11
Solution of one dimensional $\partial$ -problem      42
Spherical metric      148
Standard function      82
Stereographic projection      11
Stokes’s theorem      5
surface      143
Symmetry principle      135
Taylor — Maclaurin series      29
Topological space      143
topology      143
Total curvature      165
Transcendental entire function      94
Transcendental meromorphic function      95
Trivial zeros      215
Uniformization theorem      96
Unit ball      169
Unitary group      180
Univalent      22
Von Magoldt function      219
Weierstrass factorization theorem      101
Weierstrass formula      210
Weierstrass M-test      26
Weierstrass theorem      85

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